Answer: ( P - 10 )/12, (2x + 5)(4x + 1)
Step-by-step explanation:
The length of the rectangle = 4x + 1,
The breadth = 2x + 5
Formula for finding perimeter of a rectangle, = 2( L + B )
Now, substitute for L and B in the formula, open the formula and simplify,
= 2(4x + 1 + 2x + 5 )
= 2(6x + 5 )
= 12x + 10
Therefore, the perimeter (p)of the rectangle, = 12x + 10.
If P = 12x + 10
12x = P - 10
x = ( P - 10 )/12
Area of a rectangle = L x B
=( 4x + 1 )( 2x + 5)
We therefore open the brackets
(4x + 1)(2x + 5)= 4x X 2x + 4x X 5+ 1 X 2x + 1 X 5
= 8x² + 20x + 2x + 5
A = 8x² + 22x + 5
A = (2x + 5)(4x + 1)
Well the first one is obtuse and more than 90 degrees, the 2nd one is also obtuse and more than 90 degrees, the 3rd one is acute and less than 90 degrees, the 4th one is obtuse and 180 degrees, and the 5th one is a right angle and is 90 degrees
Answer:12
Step-by-step explanation:
we know all it's doing is adding 6 over again to each term to get the next one, so then
now for the explicit one
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=7\\ d=6 \end{cases} \\\\\\ a_n=7+(n-1)6\implies a_n=7+6n-6\implies \stackrel{\textit{Explicit Formula}}{\stackrel{f(n)}{a_n}=6n+1} \\\\\\ therefore\qquad \qquad f(10)=6(10)+1\implies f(10)=61](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%20%5C%5C%5C%5C%20a_n%3Da_1%2B%28n-1%29d%5Cqquad%20%5Cbegin%7Bcases%7D%20n%3Dn%5E%7Bth%7D%5C%20term%5C%5C%20a_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%20d%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a_1%3D7%5C%5C%20d%3D6%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20a_n%3D7%2B%28n-1%296%5Cimplies%20a_n%3D7%2B6n-6%5Cimplies%20%5Cstackrel%7B%5Ctextit%7BExplicit%20Formula%7D%7D%7B%5Cstackrel%7Bf%28n%29%7D%7Ba_n%7D%3D6n%2B1%7D%20%5C%5C%5C%5C%5C%5C%20therefore%5Cqquad%20%5Cqquad%20f%2810%29%3D6%2810%29%2B1%5Cimplies%20f%2810%29%3D61)
